How to fill element with color in texture painting?
If you have selected your element or island with L in edit mode (selecting linked mesh), or if you have selected a vertex group in edit mode prior to entering Texture Paint mode, then you can certainly choose the Fill tool and drop paint into just that area provided you have enabled Face Selection Masking in the icon  in the 3d view header. In the Tool Options panel, you can choose how much bleed area you get past that selection, and you can choose to use or not use Cavity masking there as well if you are wanting some degree of edge wear.

For painting a pattern in a brush only in that area, the best mapping method here would be '3D' so that the pattern could be connected later to another part of the painting, respecting the mesh normals.